Question
If tan−1(x)+tan−1(y)+tan−1(z)=π, then 1xy+1yz+1zx=
Answer: Option B
:
B
tan−1(x)+tan−1(y)+tan−1(z)=π
⇒tan−1x+tan−1y=π−tan−1z
⇒x+y1−xy=−z⇒x+y=−z+xyz
⇒x+y+z=xyz
Dividing by xyz, we get
1yz+1xz+1xy=1.
Note: Students should remember this question as a formula.
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:
B
tan−1(x)+tan−1(y)+tan−1(z)=π
⇒tan−1x+tan−1y=π−tan−1z
⇒x+y1−xy=−z⇒x+y=−z+xyz
⇒x+y+z=xyz
Dividing by xyz, we get
1yz+1xz+1xy=1.
Note: Students should remember this question as a formula.
Was this answer helpful ?
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